In the present work phase boundaries are considered as sharp interfaces and thus are treated as discontinuities, in particular as undercompressive shocks.
These undercompressive shock waves are not of Lax type and hence are lacking the usual uniqueness properties.
However, uniqueness can be restored by prescribing an additional algebraic relation. Although this choice remains non-unique there is a preferred choice based on physical considerations.
For further reading we refer to Refs. [1]}, [2]}, [3]}.
